Solve for $x$ and $y$ using elimination. ${2x+6y = 44}$ ${x+5y = 30}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${2x+6y = 44}$ $-2x-10y = -60$ Add the top and bottom equations together. $-4y = -16$ $\dfrac{-4y}{{-4}} = \dfrac{-16}{{-4}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {2x+6y = 44}\thinspace$ to find $x$ ${2x + 6}{(4)}{= 44}$ $2x+24 = 44$ $2x+24{-24} = 44{-24}$ $2x = 20$ $\dfrac{2x}{{2}} = \dfrac{20}{{2}}$ ${x = 10}$ You can also plug ${y = 4}$ into $\thinspace {x+5y = 30}\thinspace$ and get the same answer for $x$ : ${x + 5}{(4)}{= 30}$ ${x = 10}$